Will someone show me how to set this up?

Question

Suppose the 2/5 life of a chemical compound is 873 years.

a) How much (what fraction) remains after 271,390 years.
b)when will 1/500 of the original amount remain?

I don't want the answers I want to do the work myself but i have no clue where to start. Please help.

Answer 1

If Po = original amount then P = 2/5 Po = Poe-kt , where k is a constant to be determined and t is the time in years. So find k by setting 2/5 = e-^873k.

Once you have numerical value for k, substitute it for k to get your general equation.

Use general equation to solve remaining questions.

Answer 2

I think you need to start with an equation that relates the fraction left to the number of years in existance. So if,

T = total life of a compound
x = Fraction of the life of a compound
t = number of years in existance

Then,

t = x*T

Plug in what is known to find the total life expectancy:

873 = (2/5)*T

Solve for T

I think that you can now find the rest of you answers.